9.1 Inverse & Joint Variation

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Presentation transcript:

9.1 Inverse & Joint Variation p.534 What you should learn: Goal 1 Write and use inverse variation models, as applied in Example 4. Goal 2 Write and use Joint variation models, as applied in Example 6. 9.1 Inverse $ Joint Variation

Just a reminder from chapter 2 Direct Variation Use y = kx Means “y varies directly with x.” k is called the constant of variation. 9.1 Inverse $ Joint Variation

New stuff! Inverse Variation “y varies inversely with x.” k is the constant of variation. 9.1 Inverse $ Joint Variation

Hint: Solve the equation for y and take notice of the relationship. Ex: tell whether x & y show Direct Variation, Inverse Variation, or neither. xy=4.8 y=x+4 Inverse Variation Hint: Solve the equation for y and take notice of the relationship. Neither Direct Variation 9.1 Inverse $ Joint Variation

Ex: The variables x & y vary inversely, and y = 8 when x = 3. Write an equation that relates x & y. k=24 Find y when x= -4. y= -6 9.1 Inverse $ Joint Variation

Joint Variation When a quantity varies directly as the product of 2 or more other quantities. For example: if z varies jointly with x & y, then z=kxy. Ex: if y varies inversely with the square of x, then y=k/x2. Ex: if z varies directly with y and inversely with x, then z=ky/x. 9.1 Inverse $ Joint Variation

Part 1: The variable z varies Jointly with x & y Part 1: The variable z varies Jointly with x & y. Use the given values to write an equation relation x, y, and z. Part 2: Then find z when y = 7 and x = -4. for Part 1: Find k. for Part 2: Find z. Given values: x = -12, y = 4, z = 2 9.1 Inverse $ Joint Variation

Examples: Write an equation. y varies directly with x and inversely with z2. y varies inversely with x3. y varies directly with x2 and inversely with z. z varies jointly with x2 and y. y varies inversely with x and z. 9.1 Inverse $ Joint Variation

Assignment Page 537 # 1 – 47 odd 9.1 Inverse $ Joint Variation